f ( x ) = 91 44x 2
f ( x ) = 17
+ 18
1 Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers. Find the domain of the function
2 Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers. Find the range of the function
3 Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers. Find the domain of the function
4 Let the function f be defined by y = f (x), where x and f (x) are real numbers. Find f (8).
f (x) = 30x 20
5 Let the function f be defined by y = f (x), where x and f (x) are real numbers. Find f (7).
6 Let the function f be defined by y = f (x), where x and f (x) are real numbers. Find f (2).
7 Let the function f be defined by y = f (x), where x and f (x) are real numbers. Find f (3).
8 Evaluate the difference quotient for the function.
f (x) = 6x 5
10 Graph the function.
f (x) = 3x + 2
11 Graph the function.
f (x) = | x | 3
14 Give the domain of the function.
15 Give the range of the function.
16 Give the domain of the function.
17 The velocity of a falling object is a linear function of the time t it has been falling. If v = 18 when t = 0 and v = 130 when t = 16, express v as a function of t.
18 The amount A of money on deposit for t years in an account earning simple interest is a linear function of t. Express that function as an equation if A = $96 when t = 3 and A = $116 when t = 5.
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Name: __________________ Class: Date: _____________
19 Find the vertex of the parabolic graph of the equation.
y = 2(x 3) 2 + 7
20 Graph the quadratic function.
f (x) = x2 + 2x
f (x) = 3x2 + 4
24 Find the vertex of the parabola.
y = 8x2 + 4
y = x2 + 2x + 1
y = x2 18x + 81
y = x2 + 12x 32
y = 4x2 + 12x+ 14
29 An object is thrown from the origin of a coordinate system with the x axis along the ground and the y axis vertical. Its path, or trajectory, is given by the equation y = 296x 16x2 . Find the object's maximum height. Enter your answer as a number without units.
30 The rectangular garden in the illustration has a width of x and a perimeter of 100 feet. Find x such that the area of the rectangle is maximum.
a = 100
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Name: __________________ Class: Date: _____________
31 A farmer wants to partition a rectangular feed storage area in a corner of his barn. The barn walls form two sides of the stall, and the farmer has
34 feet of partition for the remaining two sides.
a = 34
What dimensions will maximize the area of the partition?
32 A 16 inch wide sheet of metal is to be bent into a rectangular trough with the cross section.
a = 16
Find the dimensions that will maximize the amount of water the trough can hold. That is, find the dimensions that will maximize the cross
sectional area.
33 A wholesaler of appliances finds that she can sell (1200 4p) television sets each week when the price is p dollars. What price will maximize
revenue?
34 A 270 room hotel is two thirds filled when the nightly room rate is $90. Experience has shown that each $15 increase in cost results in 30
fewer occupied rooms. Find the nightly rate that will maximize income.
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4
+ x 2
35 At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation:
s = 100t 16t2
How many seconds does it take the object to reach its maximum height?
36 At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation:
s = 224t 16t2
37 What is degree of the function
38 Graph the polynomial function
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Name: __________________ Class: Date: _____________
y = f ( x ) = x + 2 if x < 0 2 if x 0{
y = f ( x ) = x if x < 0
x 2
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x if x 0{
46 Graph the piecewise defined function.
47 Graph the piecewise defined function.
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Name: __________________ Class: Date: _____________
y = f ( x ) = 2 if x < 0 2 x if 0 x < 2 x if x 2{
y = 2x
49 Graph the function.
50 Graph the function.
51 A taxicab company charges $3 for a trip up to 1 mile, and $2 for every extra mile (or portion of a mile). Graph the ordered pairs (m, c), where m represents the miles traveled and c represents the cost.
52 A plumber charges $30, plus $40 per hour (or fraction of an hour), to install a new bathtub. Graph the points (t, c), where t is the time it takes to do the job and c is the cost.
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54 Graph the function.
55 Graph the function
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61 Graph the function
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67 Graph the equation
f (x) = 2 x + 3 , x 0
68 Graph the equation
69 Graph the equation
f ( x ) = 3x + 2
71 Find y intercept of the function
72 Graph the function
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80 Graph the function
Note that the numerator and denominator of the fraction share a common factor.
81 Graph the function
Note that the numerator and denominator of the fraction share a common factor.
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82 Graph the function
Note that the numerator and denominator of the fraction share a common factor.
83 Graph the function
Note that the numerator and denominator of the fraction share a common factor.
84 A service club wants to publish a directory of its members. An investigation shows that the cost of typesetting and photography will be $600.00, and the cost of printing each directory will be $1.00. Find the mean cost per directory if 300 directories are printed.
85 An electric company charges $7.50 per month plus $0.07 for each kilowatt hour (kwh) of electricity used. Find a linear function f (n) that gives the total cost of n kwh of electricity.
86 An electric company charges $6.50 per month plus $0.11 for each kilowatt hour (kwh) of electricity used. Find a rational function f (n) that gives the average cost per kwh when using n kwh.
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( f g ) ( x )
( g f ) ( x )
1
1
.
( g g ) ( x )
87 Let f (x) = 2x 1, g(x) = 3x 2. Find the domain of the function.
88 Let f (x) = 2x + 1, g (x) = 3x 2. Find the function.
89 Let f (x) = x 2 1, g (x) = 3x 2. Find the value of the function.
90 Let f (x) = 2x 5, g(x) = 5x 2. Find the value of the function.
91 Let f (x) = 3x 2 2, g (x) = 4x + 4. Find the value of the function.
92 Let f (x) = 3x, g (x) = x + 1. Find the composite function.
93 Let f (x) = x 2 , g(x) = 2x. Find the composite function .
94 Let . Find the composite function.
95 Let . Find the domain of the composite function.
Please express the answer in interval notation.
96 Let . Find the domain of the composite function.
Please express the answer in interval notation .
97 Let . Find the composite function.
98 Let Find the domain of the composite function.
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.
( g g ) ( x )
y = 1 7x
99 When the temperature of a pot in a kiln is F, an artist turns off the heat and leaves the pot to cool at a controlled rate of F per hour.
Express the temperature of the pot in degrees Celsius as a function of the time t (in hours) since the kiln was turned off.
100 Let Find the composite function.
101 Use the horizontal line test to determine whether the graph represents a one to one function.
102 Find the inverse of the one to one function.
y = 5x
103 Find the inverse of the one to one function.
y = 9x + 2
104 Find the inverse of the one to one function.
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Name: __________________ Class: Date: _____________
105 Find the inverse of this one to one function and graph both the function and its inverse on the same set of coordinate axes.
y = 2x
106 Find the inverse of this one to one function and graph both the function and its inverse on the same set of coordinate axes.
2x + y = 4
f ( x ) = 10
f ( x ) = x 2
f ( x ) = 7x x 6
f 1 ( x )
f ( x ) = 7 x
3 f 1 ( x )
107 Find the inverse of the one to one function and graph both the function and its inverse on the same set of coordinate axes.
108 The function is one to one on the domain Find .
109 The function is one to one on the domain . Find .
110 The function is one to one on the domain . Find .
111 Find the range of the function by finding the domain of .
112 Find the range of the function by finding the domain of .
113 A pizzeria charges $11.00 plus $0.60 per topping for a large pizza. Find a linear function that expresses the cost y of a large pizza in terms of
the number of toppings x.
114 A pizzeria charges $8.50 plus $0.65 per topping for a large pizza. Find the cost of a pizza that has 2 toppings.
115 A phone company charges $10.00 per month plus $0.02 per call. Find a rational function that expresses the average cost y of a call in a month
when x calls were made.
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Name: __________________ Class: Date: _____________
116 A phone company charges $11.90 per month plus $0.04 per call. How many calls can be made for an average cost of $0.14 per call?
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f 2( )= 17 19
1. x in ( inf, sqr(11.00000000000000000000/25.00000000000000000000)] cup [sqr(11.00000000000000000000/ 25.00000000000000000000),+ inf)
2. 3.
,( ) ,( )
x ,( ) v=7t+18 v t( )=7t+18 A=10t+66 A t( )=10t+66 3,7( )
13.
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22.
9,0( ) 6,4( ) 1.5,5( )
1369 25 17,17 4,8 8,4 150 90 $90 3.125 784 7
23.
32.
33.
34.
f n( )= 0.105n+6.500 n
0.105n+6.500 n
16x 9x+1( )
0 x 5
y= x 5
x 2( ) 9
83.
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86.
87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.
100.
101.
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104.
f x( ) 3 y=0.6x+11.0 9.8
y=0.02+ 10 x